UI Examples
What is a subset? 
Technical Answer: Set A is a
of a Set B if and only if
elements of A are also elements of B
In Other Words ...
There are two ways to be a subset
1) All the elements in Set A
in Set B
OR
2) Set A
has the
elements as B
Subsets in Pictures
All elements of Set A are contained in Set B :

Set A has the exact same elements as Set B

Subset Notation
$ \subseteq $ is the symbol for subset
Notation  Meaning 
A $\subseteq$ B  "A is the subset of B" 
B $\subseteq$ A  "B is the subset of A" 
Examples
1) Is Set A = { 2,4,6} a subset of B = {1, 2 , 3, 4, 5, 6 } 
Yes
no 
2) Is Set A = {10, 15,20} a subset of B = {10,20,30,40 } 
Yes
no 
3) Is $A=\{x: x \in \mathbb{Q}\}$ a subset of $B=\{x=\frac{1}{2},\frac{2}{3},\frac{3}{4},\cdots\}$? 
Yes
no 
4) Is $A=\{x: x \in \mathbb{R}\}$ a subset of $B=\{x: x \in \mathbb{Q}\}$? 
Yes
no 
5) Is set P = {} a subset of set M ={0,1,4,9,25,36}? 
Yes
no 
6) Is $A=\{x: x \in \mathbb{Z^+}\}$ a subset of $B=\{x: x \in \mathbb{N}\}$? 
Yes
no 
7) Is $A=\{x: x \in \mathbb{N}\}$ a subset of $B=\{x: x \in \mathbb{Z^+}\}$? 
Yes
no 
Key Ideas
I. a set is
a subset of itself
II. $\varnothing$ is a
set
of every
III. If A $\subseteq$ B and B $\subseteq$ A then
Based on this last definition are A = {1,2,3,4,5,6,7 } and B = {xx< 7 and $ x \in \mathbb{N} \ $} equal? 
Yes
no 
Practice Problems
1) Is {y } $ \subseteq $ {y}? 
Yes
no 
2) Is Set A = { y } $ \in Set B= $ {y {y} }? 
Yes
no 
3) Is Set A = {y} $ \subseteq Set B= $ { y , {y} }? 
Yes
no 